Grid structure

ABSTRACT

A grid structure formed from a plurality of building blocks, the grid structure comprising: a plurality of flat panels, wherein two of the plurality of flat panels are paired in parallel to have one of the two parallel flat panels provide an inner surface to one building block from the plurality of building blocks and the other of the two parallel flat panels provide an inner surface to another building block from the plurality of building blocks, wherein within each of the plurality of building blocks, the inner surfaces of any two adjacent panels lie on planes intersecting along a straight line that passes through an inner corner of the building block.

RELATED APPLICATIONS

This application is a national stage application, under 35 U.S.C. §371of International Patent Application No. PCT/SG2014/000132, filed on Mar.17, 2004 and published as WO 2014/142763 on Sep. 18, 2014, which claimspriority to U.S Provisional Patent Application No. 61/789,380, filed onMar. 15, 2013, which is hereby incorporated by reference in itsentirety.

TECHNICAL FIELD

The invention relates to a grid structure, a method for determininggeometry of a flat panel, and a method for forming a grid structure.

BACKGROUND

Grid structures are lattice structures that can span over relativelylarge spaces using little material compared to conventional wall-ceilingor column-beam structures. Grid structures in the form of gridshellshave been widely used to construct hangars, domes, and pavilions thatrequire uninterrupted covered space. Gridshells save material by usingdouble-curved surfaces that follow the lines of structural thrust,thereby achieving economical, efficient and elegant structures.

The use of double-curved surfaces, however, also introduces considerablechallenges for the design and fabrication of such grid structures.Freeform gridshells tend to produce variable and complex structuraljoints between load-bearing beams. For example in parabolic or otherwisevariable curvature, unique joints are required at every node of thegridshell.

Conventionally, there are several ways of achieving variable curvaturein such structures. One of the commonly used methods requires thefabrication of unique angled joints. As shown in FIG. 14, the structuralbeams may be straight. The curvature of the gridshell is achievedthrough the use of a large number of uniquely angled joints, for exampleball joints, at every node of the gridshell for joining the straightstructural beams. Constructing such joints is costly, requires strongmaterials (e.g. steel), and requires advanced machinery capable ofmilling customised three-dimensional elements.

Another conventional method requires restricting the grid to arectangular grid, i.e. subdividing a complex curved form into a grid ofX and Y structural axes. As shown in FIG. 15, flat beams follow the axesand connect structurally at intersections. In this method, each flatbeam is required to be uniquely cut in accordance with the curvature ofthe section it is to be fitted. The method is not suitable for linenetworks composed of irregular n-gons.

In yet another method as shown in FIG. 16, the gridshell is formed froma plurality of long continuous beams. The plurality of long continuousbeams are typically connected into a flat grid on the ground, and thengradually erected into shape by pushing in the, supporting edges onsite. This requires space and supporting ground, setting constraints onwhere such structures can be built. The continuity of the membersfurther restricts the kinds of line networks that can be used in thismethod. For example, the method is not suitable for line networkscomposed of irregular n-gons. There are also important constraints inthe erection of such gridshells.

In another method as shown in FIG. 17, the gridshell curvature isachieved through the use of curved structural beams with uniquely cutedges for joining with other curved structural beams. In this method,the curved structural beams typically require 3D fabrication, which canbe costly and restrictive.

A need therefore exists to provide a grid structure which will overcomeat least some of the limitations of the above conventional methods.

SUMMARY

According to one aspect, there is provided a grid structure formed froma plurality of building blocks, the grid structure comprising: aplurality of flat panels, wherein two of the plurality of flat panelsare paired in parallel to have one of the two parallel flat panelsprovide an inner surface to one building block from the plurality ofbuilding blocks and the other of the two parallel flat panels provide aninner surface to another building block from the plurality of buildingblocks, wherein within each of the plurality of building blocks, theinner surfaces of any two adjacent panels lie on planes intersectingalong a straight line that passes through an inner corner of thebuilding block.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments of the invention will be better understood andreadily apparent to one of ordinary skill in the art from the followingwritten description, by way of example only, and in conjunction with thedrawings. The drawings are not necessarily to scale, emphasis insteadgenerally being placed upon illustrating the principles of theinvention, in which:

FIGS. 1A and 1B respectively show a perspective view and a top view of agrid structure 100 according to a first embodiment.

FIG. 2 shows a perspective view of a portion of a grid structureaccording to a second embodiment.

FIG. 3 shows a flow chart illustrating a generalised method fordetermining geometry of a flat panel according to an example embodiment.

FIGS. 4A-4E show schematic diagrams for illustrating the method fordetermining geometry of a flat panel according to the method in FIG. 3.

FIG. 5 shows a flow chart illustrating a generalised method for forminga grid structure according to an example embodiment.

FIG. 6A shows the plan view of an analogous single-wall grid structureform by 2D cut panels.

FIG. 6B and 6C show the plan and axonometric view of a double-walledgrid structure form by 2D cut panels.

FIG. 7 shows an example of an input curved line-network for forming agrid structure.

FIG. 8 shows a close up view of a portion of an input line-network.

FIG. 9 shows examples of different loops.

FIG. 10 shows a schematic diagram of the parameters computed accordingto an example implementation.

FIG. 11 shows a graphical representation of the extruded panels obtainedfrom the parameters derived from FIG. 10.

FIG. 12 shows the application of the method to achieve four differentlattice patterns on an identical surface.

FIG. 13 shows an example of the layout of the plurality of the flatpanels for cutting from a sheet material.

FIG. 14-17 show prior art grid structures.

DEFINITIONS

The following provides sample, but not exhaustive, definitions forexpressions used throughout various embodiments disclosed herein.

The term “grid structure” may refer to a lattice structure that can spanover space using little material compared to conventional wall-ceilingor column-beam structures. Grid structures in the form of gridshells areused to construct hangars, domes and pavilions that requireuninterrupted covered space. Gridshells save material by usingdouble-curved surfaces that follow the lines of structural thrust. Toillustrate, FIG. 1A shows a grid structure 100 that is built inaccordance to one embodiment.

The term “building block” may mean a basic structure coupled with othersuch basic structures to form the grid structure, each such basicstructure providing a unit of construction. In various embodiments, thebuilding block is made from flat panels coupled together to enclose aloop, whereby the shape of the building block depends on the number ofpanels used to enclose the loop. With reference to FIG. 1A, there are atotal of four building blocks 102, 104, 106, 108. The building blocks102 and 108 have five flat panels or walls to form a pentagonal shapedstructure. The building blocks 104 and 106 each have three and five flatpanels or walls to form triangular and pentagonal shaped structuresrespectively. It is understood that a building block may have n numberof flat panels or walls to form an n-gon shaped structure. Accordingly,FIG. 1A illustrates possible embodiments of building blocks that realisea grid structure.

The term “flat panel” may mean a board having any number of surfaces,wherein at least a pair of surfaces, with the largest area amongst allthe other surfaces, are on opposing surfaces. With reference to FIG. 1A,reference 104 as denotes one of the pair of such opposing surfaces,having the largest area, for one panel 104 a. When two flat panels (suchas 104 a and 106 a in FIG. 1A) are paired in parallel, so that one ofthe two panels 104 a provides an inner surface 104 as of one buildingblock 104, while the other panel 106 a provides an inner surface 106 asof another building block 106, one of the surfaces 104 asl with thelargest area from one of two such panels 104 a will face a correspondingsurface 106 as from the other of the two panels 106 a, the correspondingsurface 106 as being a surface with the largest surface area of theother panel 106 a. The opposing surfaces (for example, 104 as for thepanel 104 a) with the largest area also preferably each lie on parallelplanes which are planar, thereby giving the board its flat property. Inthe embodiment as shown in FIG. 1A, the opposing surfaces (104 as forthe panel 104 a) with the largest area are in the form of aquadrilateral. In another embodiment (not shown), the opposing surfaces(with the largest area) may be in any other regular or irregular shape.

The term “paired in parallel” may refer to two flat panels (for example104 a, 106 a in FIG. 1A) being arranged in a parallel manner such thatplanes of the largest surface area on each flat panel do not intersect.In other words, the sides with the largest surface area on both of thepaired panels are parallel to each other. In various embodiments, thearrangement is such that the resulting structure will have two opposingsurfaces that each provides an inner surface of one of two differentbuilding blocks. Throughout the entire specification, the phrase “two ofthe flat panels are paired in parallel” is used interchangeably with thephrase “two parallel flat panels”.

The phrase “one of the two parallel flat panels provide an inner surfaceto one building block from the plurality of building blocks and theother of the two parallel flat panels provide an inner surface toanother building block from the plurality of building blocks” may meanthat parallel flat panels are used to form a wall of the grid structure.One of the two panels of the parallel flat panels belongs to onebuilding block, while the other of the two panels of the parallel flatpanels belongs to another building block, so that each wall of the gridstructure is shared by two adjacent building blocks.

The phrase “wherein within each of the plurality of building blocks, theinner surfaces of any two adjacent panels lie on planes intersectingalong a straight line that passes through an inner corner of thebuilding block” may mean that two flat panels of the same building block(for example 104 a and 104 b in FIG. 1A) converge to form a corner ofthe building block. Each of the respective inner surfaces 104 as, 104 bsof the two flat panels 104 a and 104 b intersect along a straight line104 abl. The straight line 104 abl passes through the corner of thebuilding block 104 where the two flat panels 104 a, 104 b converge.

The phrase “wherein at a location where the corners of two or more ofthe plurality of building blocks meet, the straight lines that passthrough the inner corners of adjacent building blocks each lie on axesthat have different angles to one another” may mean near the vicinity ofa point in which corners of at least two or more of the plurality ofbuilding blocks (for example see FIG. 2, building blocks 204, 202)converge, the straight lines 204 bcl, 202 abl, that each pass through arespective corner of at least two or more of the plurality of buildingblocks, lie on axes that may not be parallel.

The term “polygonal structure” may mean any n-gonal shape structure madefrom building blocks having any number (n) of flat panels. Each buildingblock in the same grid structure can contain a number of panels to forma shape, where both the number of panels and shape are different thanthose of another building block in the same grid structure. Possiblepolygonal structures include, but are not limited to, triangular,quadrilateral, pentagonal, hexagonal and octagonal structures.

DETAILED DESCRIPTION

In the following description, various embodiments are described withreference to the drawings, where like reference characters generallyrefer to the same parts throughout the different views.

FIGS. 1A and 1B respectively show a perspective view and a top view of agrid structure 100 according to a first embodiment. FIG. 1B shows a topview of a centre portion of the grid structure 100 shown in FIG. 1A. Itis understood that the grid structure 100 may be a gridshell structure.

The grid structure 100 is formed from a plurality of building blocks102, 104, 106, 108. In this embodiment, the plurality of building blocks102, 104, 106, 108 are of various shape. Building blocks 102 and 108each include five flat panels or walls forming a pentagonal shapedstructure. Building block 104 includes three flat panels or wallsforming a triangular shaped structure. Building block 106 includes sixflat panels or walls forming a hexagonal shaped structure. It isunderstood that a building block may have any number of flat panels orwalls to form triangular, quadrilateral, pentagonal, hexagonal or n-gonshaped structures. FIG. 1A is provided by way of an example only.

The plurality of building blocks 102, 104, 106, 108 each comprises aplurality of flat panels. For example the first building block 102includes a first flat panel 102 a, a second flat panel 102 b, a thirdflat panel 102 c, a fourth flat panel 102 d and a fifth flat panel 102e. The second building block 104 includes a first flat panel 104 a, asecond flat panel 104 b and a third flat panel 104 c. The third buildingblock 106 includes a first flat panel 106 a, a second flat panel 106 b,a third flat panel 106 c, a fourth flat panel 106 d, a fifth flat panel106 e and a sixth flat panel 106 f. The plurality of flat panels allowsfor the gridshell structure 100 to be realised using flat material thatemploys only two dimensional cutting techniques (e.g. saws,laser-cutters, 2D CNC routers). It is understood that by two dimensionalcutting of sheet material, the sides of the flat panel are substantiallyflat and are perpendicular to the largest surfaces (for example 104 as,106 as) of the flat panels.

As shown in FIG. 1B, two of the plurality of flat panels, for example104 a and 106 a, are paired in parallel to have one 104 a of the twoparallel flat panels 104 a and 106 a provides an inner surface 104 as toone building block, such as the second building block 104, from theplurality of building blocks 102; 104, 106, 108. The other 106 a of thetwo parallel flat panels 104 a and 106 a provides an inner surface 106as to another building block, such as the third building block 106, fromthe plurality of building blocks 102, 104, 106, 108. This arrangementallows the grid structure to have double walled panels along each edgeof a line-network defining the grid structure.

In an embodiment, the two parallel flat panels 104 a, 106 a may beconnected by a spacer disposed between the two parallel flat panels 104a, 106 a. In another embodiment, the two parallel flat panels 104 a, 106a may be directly connected.

Within each of the plurality of building blocks, such as the secondbuilding block 104, two of the inner surfaces 104 as, 104 bs of twoadjacent panels 104 a, 104 b lie on planes intersecting along a straightline 104 abl that passes through an inner corner of the building block.Advantageously, the double walled panels and the straight line 104 abl,being independent of other straight lines passing through other cornersof other building blocks around a network node closest to 104 abl,allows the flexibility of realising almost any grid structure, includinga grid structure with a curved line network or a double-curved gridshellstructure, with the use of flat panels. Two or more of the straightlines, each passing through adjacent building block corners around anetwork node, lie on axes that may be nonparallel. In contradistinction,for prior art grid structures that are formed from a plurality of edgesusing single walled panels, all edges that meet at a corner of a networknode, meet in a single point and must therefore be extruded parallel toeach other. Having the same panel being shared by two adjacent loopsrestricts the flexibility of such prior art grid structures fromrealising a grid structure with a curved line network.

In an embodiment, the two adjacent flat panels 104 a, 104 b, providingthe two inner surfaces 104 as, 104 bs that lie on planes intersectingalong a straight line 104 abl that passes through the inner corner of,the building block 104, are coupled together by a joint selected fromthe group comprising a hinge, a weld, a fold, an adhesive, and afastener.

Referring back to FIG. 1A, each of the plurality of flat panels, forexample 104 a, 104 b, 104 c, include two opposite edges (for example 104ae for flat panel 104 a) that connect two corners of each of theplurality of building blocks. In this embodiment, the two opposite edgesmay be parallel because the flat panel has a trapezoidal shape. In otherembodiment, the two opposite edges may be curved, straight or have anirregular form.

FIG. 2 shows a perspective view of a portion of a grid structure 200according to a second embodiment. As shown, at a location where thecorner of two of the plurality of building blocks 202, 204 meet, thestraight line 204 bcl that passes through the corner of one of the twobuilding blocks 204 lies on an axis that may have a different angle andthat may not be parallel to the straight line 202 abl that passesthrough the corner of the other of the two building blocks 202.Advantageously, the nonparallel straight lines 204 bcl, 202 abl passingthrough different corners of different building blocks 202, 204 allowcurved grid structures to be formed.

As described above, such flat panels are manufactured using twodimensional cutting techniques, omitting the requirement to use complexjoints that require three dimensional fabrication techniques to realizesuch double-curved gridshell structures. In two dimensional cutting,each flat panel may be perpendicularly cut. In other words, theperimeter of each of the plurality of flat panels is derived from aperpendicular cut.

Consider prior art techniques, which also use flat panels to realisedouble-curved gridshell structures, but have each flat panel shared bytwo adjacent nodes. The shape and curvature constraints that such priorart techniques face to realise double-curved structures because eachflat panel is shared by two adjacent loops is alleviated by using thetwo parallel flat panels, for example 104 a and 106 a, as describedabove.

FIG. 3 shows a flow chart 300 illustrating a generalised method fordetermining geometry of a flat panel, wherein two of a plurality of flatpanels are paired in parallel to have one of the two parallel flatpanels provide an inner surface to one building block from a pluralityof building blocks of a grid structure and the other of the two parallelflat panels provide an inner surface to another building block from theplurality of building blocks of the grid structure. At step 302, a linenetwork representation of the grid structure is obtained. The linenetwork comprises a plurality of nodes where adjacent nodes areconnected by an edge, wherein a line representation of each of thebuilding blocks is formed by three or more edges connected in a loop. Atstep 304, a normal for each of the edges is determined. At step 306 aplane for each of the edges is constructed, wherein the normal of theedge and the edge lie on the plane. At step 308 the plane is offsetinward of the loop, the offset being along an axis that is perpendicularto the plane, wherein the offset plane is used to construct the innersurface of the flat panel, the inner surface facing inward of the loop.At step 310, a straight line along which the offset planes intersect isdetermined, wherein two of the inner surfaces of two of the adjacentflat panels from the same loop lie on the offset planes. The straightline passes through an inner corner of each of the plurality of buildingblocks.

FIGS. 4A-4E show schematic diagrams for illustrating the method fordetermining geometry of a flat panel according to the method above.

In FIG. 4A, a line network representation of a grid structure 400 isshown. The line network comprises a plurality of nodes 402 a, 402 b, 402c. Adjacent nodes are connected by an edge. For example, nodes 402 a and402 b are connected by edge 404 a, nodes 402 b and 402 c are connectedby edge 404 b, and nodes 402 c and 402 a are connected by edge 404 c.The edges 404 a, 404 b and 404 c are connected in a loop 406 to form aline representation of a building block for the grid structure 400. InFIG. 4A, the normals 408 a, 408 b, 408 c of respective edges 404 a, 404b, 404 c are determined.

The normals 408 a, 408 b, 408 c of each of the edges 404 a, 404 b, 404 cmay be determined or obtained by first determining the node normals (notshown) on both ends of each of the edges 404 a, 404 b, 404 c based onsurface curvature, which is desired, of the grid structure at therespective nodes 402 a, 402 b, 402 c, and averaging the node normals onboth ends of each of the edges 404 a, 404 b, 404 c to obtain the normals408 a, 408 b, 408 c of each of the edges 404 a, 404 b, 404 c.Alternatively, the normals 408 a, 408 b, 408 c of each of the edges 404a, 404 b, 404 c may be obtained from user input.

In FIG. 4B, a plane represented by coordinate axes (x_(a),y_(a)),(x_(b),y_(b)) and (x_(c),y_(c)) for each of the edges 404 a, 404 b, 404c is constructed, wherein the normal 408 a, 408 b, 408 c of each edgeand each edge 404 a, 404 b, 404 c lie on the respective plane(x_(a),y_(a)), (x_(b),y_(b)) and (x_(c),y_(c)). FIG. 4B further showsaxis z_(a), z_(b), z_(c) to represent a direction inward of the loop 406from each plane (x_(a),y_(a)), (x_(b),y_(b)) and (x_(c),y_(c)).

In FIG. 4C, the plane (x_(a),y_(a)), (x_(b),y_(b)) and (x_(c),y_(c)) isoffset towards the centre of the loop, the offset being along the axesz_(a), z_(b), z_(c) that is perpendicular to the plane (x_(a),y_(a)),(x_(b),y_(b)) and (x_(b),y_(b)). An amount to offset is determined bytaking into consideration a desired thickness of the flat panel and adesired gap between two parallel flat panels, in which one of the twoparallel flat panels provides an inner surface to one building blockfrom a plurality of building blocks of a grid structure and the other ofthe two parallel flat panels provides an inner surface to anotherbuilding block of the grid structure.

In FIG. 4D, the offset plane (x_(a),y_(a)), (x_(b),y_(b)) and(x_(c),y_(c)) is used to construct a surface of the flat panel 410 a,410 b, 410 c. At an inner corner of each of the plurality of buildingblocks, a straight line 412 a, 412 b, 412 c along which offset planesintersect is being determined. Each of an inner surface of two of theadjacent flat panels, from the same loop, lie on each of the offsetplanes.

Advantageously, the straight lines 412 a, 412 b, 412 c can be used todetermine the profile of the sides of the flat panels 410 a, 410 b and410 c, which can be joined with each other via linear joints to form oneof the plurality of building blocks. In other words, the straight line412 a, along which the flat panels 410 a and 410 c intersect, is used todetermine the profile of the respective sides of the flat panels 410 aand 410 c such that they may join to form a first corner of the buildingblock. Flat panels 410 a and 410 b intersect along straight line 412 b,and the straight line 412 b is used to determine the profile of therespective sides of the flat panel 410 a and 410 b such that they mayjoin to form a second corner of the building block. Flat panel 410 b and410 c intersect along line 412 c, and the line 412 c is used todetermine the profile of respective sides of the flat panels 410 b and410 c such that they may join to form a third corner of the buildingblock.

In FIG. 4E, the flat panel 414 a is extruded from the surface of theflat panel 410 a, in a direction outward of the loop 406 by the desiredthickness of the flat panel to obtain a three dimensional geometryrepresentation of the flat panel 414 a.

FIG. 5 shows a flow chart illustrating a generalised method for forminga grid structure according to an example embodiment. At step 502, aplurality of building blocks is formed by having, within each of theplurality of building blocks, two of the inner surfaces lie on planesintersecting along a straight line that passes through a corner of thebuilding block. At step 504, the plurality of building blocks are joinedby pairing two of a plurality of flat panels, each from a differentbuilding block, in parallel, to have one of the two parallel flat panelsprovide an inner surface to one building block from the plurality ofbuilding blocks and the other of the two parallel flat panels provide aninner surface to another building block from the plurality of buildingblocks.

Prior to step 502 above, the method may further comprise the steps ofdetermining geometry of each of the plurality of the flat panels, andcutting sheet material perpendicularly to obtain the flat panel. Thestep of determining geometry of the flat panel may adopt the method asdescribed above with reference to FIG. 3, and FIGS. 4A-E.

FIG. 13 shows an example of the layout of the plurality of the flatpanels for cutting ,from a sheet material 1300. The holes and numbercodes shown on each of the panels in FIG. 13 are illustrative only andindicate panel identification codes and holes for fastening hinges tothe panels. As can be seen, each of the plurality of the flat panels1302 is arranged adjacent to each other on the sheet material 1300. Eachof the plurality of the flat panels 1302 may then be perpendicularly cutfrom the sheet material 1300 so that individual pieces of flat panel maybe obtained. Such a perpendicular cut is performed by extracting theplurality of the flat panels 1302, from the sheet material 1300, using acut that is along a plane that is perpendicular to the sheet material1300 surface, where the cut traces the perimeter of each of the flatpanels.

Returning to step 502, in which the plurality of building blocks isformed by having, within each of the plurality of building blocks, twoof the inner surfaces of any two adjacent panels lie on planesintersecting along the straight line that passes through the innercorner of the building block, the two flat panels, that provide the twoinner surfaces, may be coupled by using a joint selected from the groupcomprising a hinge, a weld, a fold, an adhesive, and a fastener.

In step 504 above, in which the plurality of building blocks are joinedby pairing two of the plurality of flat panels in parallel, a spacer maybe disposed between the two parallel flat panels such that the twoparallel panels may be connected together with the spacer. In anotherembodiment, the two parallel panels may be connected directly.

Advantageously, various embodiments of the grid structure, method fordetermining geometry of a flat panel, and method for forming a gridstructure as described above allow the creation of grid structures outof almost any line network comprising regular or irregular n-gons,including gridshell structures and/or curved grid structures with curvedline network, in which all beams and joint elements of the gridstructure can be fabricated with only two-dimensional cuttingtechnology. The double-walled structures, along network edges of aline-network defining the grid structure, formed by the paired orparallel flat panels have allowed each flat panel to be obtained fromsimple 2D cutting technology (e.g. saws, laser-cutters, 2D CNC routers).

Further, each flat panel may be coupled to neighboring flat panel alongstraight intersection lines to form building blocks of various n-gonsshaped as described in the various embodiments, allowing flat panels tobe structurally connected using simple linear fasteners, such as hinges,welds, folds, corner brackets, adhesives etc.

Embodiments of the grid structure and methods as described above possesssignificant improvement over the conventional grid structures andmethods for creating conventional grid structures which rely on eithercomplex joints between grid structure elements, or complex edge elementsthat require 3d fabrication technology. (e.g. angular cuts).Accordingly, embodiments of the grid structure and methods describedabove enable elements (e.g. beams, joints, walls, panels, planes etc.)of a grid structure to be fabricated economically, and enable the gridstructure to be assembled from simple, pre-assembled building blocksusing unspecialized labor. Instead of relying on high-precisionfastening and assembly work on site, common to traditional gridstructures, the proposed method achieves flat panels with precisegeometric outlines on a computer controlled 2D cutter or saw, which aresimple to assemble into building blocks, and building blocks into a gridstructure. Furthermore, embodiments of the grid structure and methods asdescribed can turn almost any curved line network into a grid structure,overcoming the significant constraints that limit the shapes andcurvatures of single-walled grid structures.

To achieve this, two key features may be necessary. The structure mayneed to be composed of two parallel walls around each network edge, andthe adjoining non-parallel walls in each network loop may need to beextruded at particular angles, such that straight intersection lines areachieved on the interior planes of n-gons. Both features may benecessary to allow 2D fabrication.

FIG. 6A shows the plan view of an analogous single-wall grid structure600 form by 2D cut panels 602. As can be seen, it is not feasible toconstruct a single-wall grid structure with panels 602 fabricated withstrictly two dimensional cutting without creating gaps 604 betweenelements or modifying the input line-network. The FIG. 6B and 6C showthe plan and axonometric view of a double-walled grid structure 610,form by 2D cut panels 612. FIG. 6B and 6C show in plan and axonometricview how a continuous grid structure 610 is achieved through adouble-walled structure around each network edge, where the panels 612are extruded at such angles that straight intersection lines 614 areachieved within all interior surface planes 616, 618 of the panels ofthe grid structure loops.

As discussed above, the joints of embodiments of the grid structure areconnected along a linear intersection line between two neighbouringplanes of grid structure beams or walls, allowing any angles to bejoined as long as fasteners can fit between the planes. Since theconnection is achieved via intersecting interior planes of the walls,the vertical depth of the walls becomes a structural variable that, canbe increased for stronger linear connections. Advantageously, thisoffers a unique solution for turning almost any curved line network intoa gridshell structure in an economical way.

In an implementation, embodiments of the method for determining geometryof a flat panel, and the method for forming a grid structure may beimplemented on a computer or any processor. A computer readable mediummay have stored thereon computer code means for performing all the stepsof embodiments of the methods when said computer code means is run on acomputer.

FIG. 7 shows an example of an input curved line-network 700 for forminga grid structure such as gridshell structure. When embodiments of themethods are implemented on a computer or a processor, the computation ofthe gridshell structure starts with one user input—a curved line-network700. The line-network 700 can follow any surface curvature. All verticesor nodes 702 in the line network may be used as structural joints in thegridshell.

FIG. 8 shows a close up view of a portion of an input line-network 800.The first step in analysing the input line-network 800 is to detectwhich combinations of edges 802 form closed loops 804. If three or moreedges 802 in the line-network 800 form a cycle, then they are detectedas loops 804. It is necessary to know the loops 804 in the line-network800 in order to find the different extrusion angles for flat structuralwalls, as explained below.

Loops can be detected in complex networks on curved three-dimensionalsurfaces. Loops may comprise of regular or irregular polygons of anysize (n-gons) and shape. FIG. 9 shows examples of different loops. Forexample, triangular loop 902, n-gons loop 904, equilateral loop 906.

After loops have been detected, computation of the geometry ofstructural panels begins. These panels obtained from computation mayeventually be cut out of sheet material on a two-dimensional cutter.

As previously discussed, embodiments of the grid structures form twopaired flat panels or double-walled panels along each input networkline. Facing panels along the same edge are preferably set completelyparallel to each other and the geometries of panels in the same loopthat share a corner are extruded such that a straight intersection lineis achieved between all neighbouring interior planes of the n-gons,allowing the latter to be fastened with straight connectors (e.g.hinges, welds, folds, corner brackets, adhesives, fasteners etc.).

In this implementation, the computer or processor will determine edgenormals (e), loop-edge vectors (d), loop-edge planes (F), and loop-nodevectors (l), for the entire input network.

FIG. 10 shows a schematic diagram of the parameters computed accordingto an example implementation.

First, node normals (n) are given from the input line network at theedge intersection points (P). The vectors of node normals are given asthe underlying surface normals at points (P).

Second, the node normals at the opposite ends of each original networkedge (for example a first normal vector 1002 a and a second normalvector 1002 b for a first edge 1004 a, and for example the first normalvector 1002 a and a third normal vector 1002 c for an adjacent secondedge 1004 b; for example, the first normal vector 1002 a may be thenormal vector corresponding to the node 1006 a that the first edge 1004a and the second edge 1004 b have in common; in other words: where thefirst edge 1004 a and the second edge 1004 b intersect) are used toderive the corresponding edge normal (e). Each edge normal is found asthe average of its two endpoints normals: e_(i)=(n_(i)+n_(i+1))/2.

Next, a loop-edge plane (F) is constructed (for example a first planefor the first edge 1004 a and a second plane for the adjacent secondedge 1004 b) from the original edge normal (e) and the loop-edge vector(d) for the adjacent second edge 1004 b) such that that F_(i).x=e_(i),and F_(i).y=d_(i). The normal vector of this plane (F_(i).z) is used tooffset the loop plane inside, by at least the thickness of theconstruction material (e.g. steel plate). Typically, an additional gapis desirable between the parallel panels in order to leave space forfasteners on both sides of the structural planes.

The loop-node vector (l) is calculated as the intersection line of twoadjacent and offset loop-edge planes (l_(i)=F_(i) intersection withF_(i-1)) (for example as intersection 1010 a of the first offset plane1012 a and the second offset plane 1012 b). The panels may be cut toresemble the desired shape according to the cutting line. Everyloop-node vector (l) is in the same plane with both of its neighbouringloop-edge vectors (l_(i) is coplanar with l_(i−1) and l_(i+1)). Thesevectors (l_(i) and l_(i+1)) and the loop-edge plane (F_(i)) are used toconstruct a structural panel, which represents the inner materialsurface of each loop.

The surfaces are extruded outwards from each loop to achieve a desiredmaterial thickness for the structural panels. FIG. 11 shows a graphicalrepresentation of extruded panels 1100 obtained from the parametersderived above, the extruded panels 1100 being a trapezoidal shapedpanel. Since all structural panels 1100 share an inner edge (alongvector l the panels may be cut along the determined cutting line so thatthey fit together using standard linear connectors and so that theboundaries of the panels follow the linear vector l) with theirneighbouring edges, they can be joined to each other using standardlinear connectors that follow the linear vector (l) on the inner surfaceof a loop.

Both the desired vertical depth (which is an approximation since depthon both ends of the panels is different due to their trapezoidal shapethat generates the gridshell's curvature) and the offset distancebetween two parallel panels are design variables that a user cancontrol. User input for the depth of the shell sets the depth at thelower end of the trapezoid.

Since the paths of forces in gridshells are generally designed to followthrough the midpoints of structural elements, the loop edges typicallyneed to be extruded vertically in both directions above and below theiroriginal axes in the input line network. Once the height of eachtrapezoidal panel is computed, the trapezoids are offset towards thecentre of each loop to form the inner surfaces of the structural loops.The offset distance accounts for the material thickness of the walls andthe desired gap size between two parallel walls.

Once the edge surfaces are extruded and populated throughout thestructure, a double curved surface is formed from flat edge panels.

Embodiments of the methods can be used to generate gridshell latticesfor line-networks of different curvatures and patterns. FIG. 12 showsthe application of the method to achieve or obtain four differentlattice patterns on an identical surface.

Embodiments of the grid structure and methods allow one to generatesupport structures for free-form line-networks on curved surfaces usingstrictly flat members, which can be cut on two-dimensional routers.Thus, it can be seen that the limitations in conventional approaches, inwhich either edges (e.g. beams, walls) or nodes (e.g. joints,connections) require cutting in more than two dimensions, or the networkpattern is limited to rectangular grids, have been overcome in thevarious embodiments described.

Embodiments of the grid structure and methods may be used to generategridshell structures for buildings (e.g. canopies, hangars, pavilions,etc.) for functions that benefit from large, unobstructed covered spaces(assembly activities, airplane covers, storage, sports activities,agricultural acitivites, etc.). Beyond structural efficiency, gridshellceilings are also aesthetic to look at and can be applicable in varioussettings.

Besides full-scale architectural application, embodiments of the gridstructure and methods may be used to develop, three-dimensional assemblykits, educational toys for children and architectural scale models. Themethod can be used to develop 3D gridshell modela in shapes ofwell-known buildings (e.g. Beijing Olympic Stadium and Aquatic Stadium;Allianz Arena in Munich; London City Hall etc.) that can be assembledfrom pre-fabricated flat sheet material (e.g. plastic, wood, or metal,or composites panels). Ensuring that all the gridshell elements are cuton simple 2D cutters (e.g. lasercutters) makes the application extremelyaffordable and visually spectacular.

Notwithstanding the claimed subject-matter, embodiments are alsodescribed by the following clauses:

-   1. A method for determining a cutting scheme for cutting a plurality    of panels, so that the panels form a gridshell, the gridshell    comprising a curved surface and comprising a plurality of beams,    each beam comprising two parallel panels, the method comprising:

determining a representation of a surface, the representation of thesurface comprising a network of edges and normal vectors, the networkcomprising a plurality of nodes and at least one loop of nodes, whereineach normal vector of a plurality of normal vectors is assigned to onenode of the plurality of nodes;

for each loop of the at least one loop of nodes:

-   -   determining a representation of a first vector based on a first        node of the respective loop and a second node of the respective        loop;    -   determining a representation of a second vector based on a first        normal vector assigned to the first node and a second normal        vector assigned to the second node;    -   determining a first plane based on the first vector and the        second vector;    -   determining a first offset plane based on the first plane and a        first offset pointing inwards the loop;    -   determining a representation of a third vector based on the        first node and a third node of the respective loop;    -   determining a representation of a fourth vector based on the        first normal vector and a third normal vector assigned to the        third node;    -   determining a second plane based on the third vector and the        fourth vector;    -   determining a second offset plane based on the second plane and        a second offset pointing inwards the loop;    -   determining cutting lines for a first panel and for a second        panel based on an intersection of the first offset plane and the        second offset plane.

-   2. The method of clause 1, wherein a normal vector of the plurality    of normal vectors approximates a normal vector of the surface at the    position of the node assigned to the normal vector.

-   3. The method of clause 1 or 2, wherein the first vector is    determined based on a difference of the first node and the second    node.

-   4. The method of any one of clauses 1 to 3, wherein the first vector    is determined as a vector connecting the first node and the second    node.

-   5. The method of any one of clauses 1 to 4, wherein the second    vector is determined as an average of the first normal vector and    the second normal vector.

-   6. The method of any one of clauses 1 to 5, wherein the first plane    is determined as a plane having a first dimension along the first    vector and having a second direction along the second vector.

-   7. The method of any one of clauses 1 to 6, wherein the first offset    plane is determined as a plane parallel to the first plane in a    distance of the first offset from the first plane.

-   8. The method of any one of clauses 1 to 7, wherein the third vector    is determined based on a difference of the first node and the third    node.

-   9. The method of any one of clauses 1 to 8, wherein the third vector    is determined as a vector connecting the first node and the third    node.

-   10. The method of any one of clauses 1 to 9, wherein the fourth    vector is determined as an average of the first normal vector and    the third normal vector.

-   11. The method of any one of clauses 1 to 10, wherein the second    plane is determined as a plane having a first dimension along the    third vector, and having a second direction along the fourth vector.

-   12. The method of any one of clauses 1 to 11, wherein the second    offset plane is determined as a plane parallel to the second plane    in a distance of the second offset from the second plane.

-   13. The method of any one of clauses 1 to 12, wherein the first    offset is equal to the second offset.

-   14. The method of any one of clauses 1 to 13, wherein the cutting    line is determined as the intersection of the first offset plane and    the second offset plane.

-   15. A part for a gridshell, wherein the part comprises a panel cut    according to a cutting line determined according to the method of    any one of clauses 1 to 14.

-   16. A part for a gridshell, the part comprising:

a panel, wherein a first side of the panel is parallel to a second sideof the panel, and wherein each of a third side of the panel, a fourthside of the panel, a fifth of the panel and a sixth side of the panelare perpendicular to the first side.

-   17. A gridshell comprising:

a plurality of beams; and

a plurality of connectors, each connector comprising a linear fastener;

wherein each beam comprises two parallel panels;

wherein the panels of the plurality of beams are arranged in a pluralityof loops;

wherein the two parallel panels of each beam belong to two differentloops;

wherein for each panel a first side of the panel is parallel to a secondside of the panel, and wherein each of a third side of the panel, afourth side of the panel, a fifth side of the panel and a sixth side ofthe panel are perpendicular to the first side; and

wherein in each loop, a connector of the plurality of connectorsconnects two panels of the loop.

-   18. The gridshell of clause 17, wherein each connector of the    plurality of connectors connects two planes along a single    intersection line and comprises at least one of a hinge, a weld, a    fold, an adhesive, and a fastener.-   19. The gridshell of clause 18, wherein the third side is parallel    to the fourth side.-   20. The gridshell of any one of clauses 17 to 19, wherein the    distance between the first side and the second side is smaller than    the distance between the third side and the fourth side.-   21. The gridshell of any one of clauses 17 to 20, wherein the panel    and the parallel further panel are provided at a pre-determined    distance.-   22. The gridshell of clause 21, wherein the pre-determined distance    is in the order of a thickness of a spacer block that can be    positioned between two parallel panels.-   23. The gridshell of any one of clauses 17 to 22, further    comprising:

a further connector configured to connect the two parallel panels of abeam.

-   24. The gridshell of clause 23, wherein the further connector    comprises a spacer block.-   25. A gridshell comprising a plurality of parts for a gridshell    according to clause 15.-   26. A gridshell comprising a plurality of parts for a gridshell    according to clause 16.

It will be understood that the determinations or properties givenaccording to a function in the above clauses (for example “average” or“difference” or “equal” or “intersection” or “parallel”) may beunderstood as to involve a determination or a property of at leastessentially the function. For example, instead of determining “a−b” fora difference of a and b, “a−b+eps” may be determined, with eps being asmall positive or negative number (for example an order of magnitudesmaller than a or than b or than a−b, for example at least a factor of10 smaller than a or than b or than a−b).

A device for performing the method for determining a cutting scheme maybe provided.

A panel may also be referred to as a board, plate or other element cutout of flat sheet material. The panel may be made of any material, forexample wood, plastic, metal, or paper.

The distance between the first side of a panel and the second side ofthe panel may be the thickness of the panel.

By determining the cutting line for a plurality of panels, the panelsmay be used to resemble (or approximate) the surface in the form of agridshell, wherein two panels may be provided in parallel as a beam. Thebeam may follow the edges of the grid. The ends of the panels may belocated near the nodes of the grid.

According to the method for determining a cutting scheme, cutting linesmay be determined for a first panel which may be one panel of the twoparallel panels that form a beam from the first node to the second node,and, for a second panel which may be one panel of the two parallelpanels that form a beam from the first node to the third node.

According to the method for determining a cutting scheme, the secondvector may be determined as an average of the first normal vector andthe second normal vector. For example, the direction of the secondvector may be determined as an average of the first normal vector andthe second normal vector.

Each panel may have a length, which may be a size of the panel at leastessentially from one intersection to another intersection. Each panelmay have a width, which may be a size at least essentially along thedirection of the second vector. The width of each panel may bedetermined based on a user input; for example, a user may determine thewidth of each panel. The width of different panels may be different. Thewidth of the panels may determine the thickness of the gridshell. Thethickness of the gridshell may be different for different portions ofthe gridshell.

Each panel may have a thickness, which may be a size of the panel in adirection at least essentially orthogonal to the direction of the lengthof panel and at least essentially orthogonal to the direction of thewidth of the panel.

The thickness of each panel may have an influence of the intermediaryspace at the interconnection of several panels.

The thickness of each panel may be chosen so that it is thick enough toprovide stability, but yet not too thick in order to avoid overlappingof several panels in a loop or at an interconnection of several panels.

By determining the cutting line according to the method for determininga cutting scheme for cutting a plurality of panels, the cutting linesfor a panel may be determined. This may include determining an angle atwhich a side of the panel is to be cut, and furthermore may include aposition on the panel at which to cut the panel at the determined angle.In other words, for a trapezoidal shape of the panel, not only theangles of the non-parallel sides may be determined, but also the lengthsof the two parallel sides.

Furthermore, it will be understood that the panels may have any shapeother than trapezoidal shape, as long as the angles for two sidesadjacent to a side which forms the outer shape of the gridshell, aredetermined like described above.

The cutting lines may define the three-dimensional shape of theresulting gridshell.

At the boundaries of the surface (for example at the portions of thesurface where the surface reaches ground level, or for openings such asdoors or windows of the surface), the loops may be incomplete. Forexample, for openings, for a complete loop next to the opening, a beammay include two panels, wherein one of the two panels belongs to thecomplete loop, and the other one of the two panels does not belong to acomplete loop. However, both of the two panels may be cut according tothe method described above.

A network may also be referred to as a grid, or as a mesh.

The different lengths of two panels of a beam may influence theorientation of the beam in two dimensions, and the angle at Which thepanel is cut according to the cutting line may influence the orientationof the beam in a third dimension.

The cutting line may define how to cut a panel, and the cut may beperpendicular to the first side of the panel.

Providing a part of a gridshell in which a first side of the panel isparallel to a second side of the panel, and in which each of a thirdside of the panel, a fourth side of the panel, a fifth side of the paneland a sixth side of the panel are perpendicular to the first side allowsfor easy cutting of any panel of a pre-determined thickness to be in theform of the part of the gridshell. For example, a panel may be cut by atwo-dimensional (2D) cutter, in which the cutting is always performedperpendicular to the first side and the second side, so that only twocoordinates (which may be determined according to the cut line) may berequired to identify the cut, and so that standard 2D cutters, like alaser-cutter, water-jet cutter, turret-cutter, flat-bed CNC cutter,circular saw, a buzz saw, a band saw, a belt saw, a coping saw, afretsaw, a inlay saw, a jigsaw, a scroll saw, or any other kind of sawmay be used.

In a loop of nodes, there may be edges from one node to another node.The edges may intersect only at the nodes. For example, nodes and edgesof the loop may define a polygon. For example, the angle of two edgesmay be less than 180 deg (or less than pi rad). It will be understoodthat an edge of the loop may define a direction pointing outwards thepolygon (in other words: outwards the loop) and a direction pointinginwards the polygon (in other words: inwards the loop).

It will be appreciated by a person skilled in the art that numerousvariations and/or modifications may be made to the present invention asshown in the embodiments without departing from a spirit or scope of theinvention as broadly described. The embodiments are, therefore, to beconsidered in all respects to be illustrative and not restrictive.

The invention claimed is:
 1. A grid structure formed from a plurality ofbuilding blocks, the grid structure comprising: a plurality of flatpanels, wherein two of the plurality of flat panels are paired inparallel to have one of the two parallel flat panels provide an innersurface to one building block from the plurality of building blocks andthe other of the two parallel flat panels provide an inner surface toanother building block from the plurality of building blocks, whereinwithin each of the plurality of building blocks, inner surfaces of thebuilding block provided by any two adjacent panels lie on planes thatintersect along a straight line, defined by edges of the two adjacentpanels, that passes through an inner corner of the building block,wherein at a location where corners of two or more of the plurality ofbuilding blocks meet, the straight lines that pass through the innercorners of adjacent building blocks each lie on axes that have differentangles to one another, wherein within at least two of the plurality offlat panels that are paired, the edges of the paired flat panels whichare closest each lie on axes that have different angles to one another.2. The grid structure of claim 1, wherein the plurality of buildingblocks comprises different polygonal structures.
 3. The grid structureof claim 2, wherein the polygonal structures comprises any one or moreof the following shapes: triangular, quadrilateral, pentagonal andhexagonal.
 4. The grid structure of claim 1, wherein two opposite edgesof each of the plurality of building blocks that connect two corners ofeach of the plurality of building blocks are parallel.
 5. The gridstructure of claim 1, wherein each of two opposite edges of each of theplurality of building blocks that connect two corners of each of theplurality of building blocks are curved or straight.
 6. The gridstructure of claim 1, wherein the perimeter of each of the plurality offlat panels is derived from a perpendicular cut.
 7. The grid structureof claim 1, wherein the two parallel flat panels are connected by aspacer disposed between the two parallel flat panels.
 8. The gridstructure of claim 1, wherein the two parallel flat panels are directlyconnected.
 9. The grid structure of claim 1, wherein the grid structureis a gridshell.
 10. The grid structure of claim 1, wherein the two flatpanels, providing the two inner surfaces that lie on planes intersectingalong a straight line that passes through the inner corner of thebuilding block, are coupled together by a linear joint selected from agroup comprising a hinge, a weld, a fold, an adhesive, and a fastener.11. A method for determining geometry of a flat panel, wherein two of aplurality of flat panels are paired in parallel to have one of the twoparallel flat panels provide an inner surface to one building block froma plurality of building blocks of a grid structure and the other of thetwo parallel flat panels provide an inner surface to another buildingblock from the plurality of building blocks of the grid structure, themethod comprising: obtaining a line network representation of the gridstructure, the line network comprising a plurality of nodes whereadjacent nodes are connected by an edge, wherein a line representationof each of the building blocks is formed by three or more edgesconnected in a loop; determining a normal for each of the edges;constructing a plane for each of the edges, wherein the normal of theedge and the edge lie on the plane; offsetting the plane inward of theloop, the offset being along an axis that is perpendicular to the plane,wherein the offset plane is used to construct the inner surface of theflat panel, the inner surface facing inward of the loop; and determininga straight line along which the offset planes intersect, wherein two ofthe inner surfaces of two of the adjacent flat panels from the same looplie on the offset planes, wherein the straight line passes through aninner corner of each of the plurality of building blocks, wherein at alocation where the corners of two or more of the plurality of buildingblocks meet, the straight lines that pass through the inner corners ofadjacent building blocks each lie on axes that have different angles toone another.
 12. The method of claim 11, wherein the step of offsettingthe plane further comprises determining an amount to offset by takinginto consideration the thickness of the flat panel and the gap betweenthe two parallel flat panels.
 13. The method of claim 11, wherein thestep of determining a normal for each of the edges further comprises thestep of: determining node normals on both ends of each of the edgesbased on a surface curvature of the grid structure; and obtaining theedge normal by averaging the node normal on both ends of each of theedges.
 14. The method of claim 11, further comprising the step ofextruding the surface of the flat panel in a direction outward of theloop by the desired thickness of the flat panel to obtain a threedimensional geometry representation of the flat panel.
 15. A method forconstructing a grid structure formed from a plurality of buildingblocks, the method comprising: forming the plurality of building blocksby having, within each of the plurality of building blocks, two innersurfaces of any two adjacent panels lie on planes intersecting along astraight line that passes through an inner corner of the building block;and joining the plurality of building blocks by pairing two of aplurality of flat panels, each from a different building block, inparallel, to have one of the two parallel flat panels provide an innersurface to one building block from the plurality of building blocks andthe other of the two parallel flat panels provide an inner surface toanother building block from the plurality of building blocks, wherein ata location where the corners of two or more of the plurality of buildingblocks meet, the straight lines defined by edges of the two adjacentpanels that pass through the inner corners of adjacent building blockseach lie on axes that have different angles to one another, whereinwithin at least two of the plurality of flat panels that are paired,adjacent edges of the flat panels each lie on axes that have differentangles to one another, and wherein within at least two of the pluralityof flat panels that are paired, the edges of the paired flat panelswhich are closest each lie on axes that have different angles to oneanother.
 16. The method of claim 15 further comprising: determining thegeometry of each of the plurality of the flat panels; and cutting sheetmaterial perpendicularly to obtain the flat panels.
 17. The method ofclaim 16, wherein the step of determining the geometry of the flat panelfurther comprises: obtaining a line network representation of the gridstructure, the line network comprising a plurality of nodes whereadjacent nodes are connected by an edge, wherein a line representationof each of the building blocks is formed by three or more edgesconnected in a loop; determining a normal for each of the edges;constructing a plane for each of the edges, wherein the normal of theedge and the edge lie on the plane; and offsetting the plane inward ofthe loop, the offset being along an axis that is perpendicular to theplane, wherein the offset plane is used to construct the inner surfaceof the flat panel, the inner surface facing inward of the loop, whereineach of the straight lines that pass through the inner corners ofadjacent building blocks is formed by determining, within two of theinner surfaces of two of the adjacent flat panels from the same loopthat lie on the offset planes, a straight line along which the offsetplanes intersect.
 18. The method of claim 15, wherein the step offorming the plurality of building blocks by having, within each of theplurality of building blocks, two of the inner surfaces of any twoadjacent panels lie on planes intersecting along the straight line thatpasses through the inner corner of the building block further comprisescoupling the two flat panels, that provide the two inner surfaces, usinga joint selected from a group comprising a hinge, a weld, a fold, anadhesive, and a fastener.
 19. The method of claim 15, wherein the stepof joining the plurality of building blocks by pairing two of theplurality of flat panels in parallel further comprises disposing aspacer between the two parallel flat panels.
 20. The method of claim 15,wherein the step of joining the plurality of building blocks by pairingtwo of the plurality of flat panels in parallel further comprisesdirectly connecting the two parallel flat panels.